Could you maybe do one transition at a time? Start by moving him to the cot while he is still being wrapped and get him used to the cot for a few weeks, and once he has adjusted then start putting him in the grobags? Although there is a gap you can still wrap him and then put a sheet over the top tucked into the cot IYKWIM - I did this with Iz when she was in her grobag - with a sheet over her to keep her snug. He will eventually get used to having his arms out- most people find a gradual loosening of the wrap works well and once they have adjusted to no wrap then move them to the bag. We changed straight over from wrapping to a bag at 8 weeks but she didn't have a dummy to knock out.
Good luck!